Quant III and Bayesian Measurement
December 4, 2023
How representative is a government of its people?
Anonymous records of what candidate each voter picked in each race on the ballot
Modelling challenges
Categorical outcome with different options for each race
People vote in different races
1.3B “bubbles” and 50m voters in 2020 election
Continuous, latent outcome with categorical indicators –> IRT model
| Quantity | Symbol |
|---|---|
| Individual | \(j = 1, 2, …, J\) |
| Race | \(k = 1, 2, …, K\) |
| Candidate | \(c = 1, 2, …, C\) |
| Ideal point of voter \(j\) | \(\alpha_j\) |
| Discrimination/Slope Parameter | \(\gamma_{k(c)}\) |
| Difficulty/Location Parameter | \(\beta_{k(c)}\) |
The scale and location of \(\alpha\) are unidentified (can add or multiply a constant with no change in likelihood)
\(\gamma\)’s sign can also flip around with relation to the sign of \(\alpha\).
Priors
Uninformative, standard priors for other parameters
Future work: Informative priors using party or NOMINATE/DIME scores to help with identification and speed convergence
Informative priors from DIME or NOMINATE scores
Multiple dimensions
Connect this better to a question about representation
Reece – CVR Ideals